# Collinear order and chirality-reorientation transition in the Cairo pentagonal magnet Bi$_4$Fe$_5$O$_{13}$F

## TL;DR

This study reveals how interlayer spins influence 3D magnetic order and induce spin-reorientation transitions in the Cairo pentagonal magnet Bi$_4$Fe$_5$O$_{13}$F, highlighting the role of anisotropy and chirality.

## Contribution

It uncovers the dual role of interlayer spins in mediating magnetic order and transitions, emphasizing the importance of single-ion anisotropy in this complex magnet.

## Key findings

- Identification of two orthogonal magnetic structures with opposite chiralities
- Discovery of an intermediate nearly collinear disordered phase
- Demonstration of strong single-ion anisotropy controlling local chirality

## Abstract

We show that interlayer spins play a dual role in the Cairo pentagonal magnet Bi$_4$Fe$_5$O$_{13}$F, on one hand mediating the three-dimensional (3D) magnetic order and on the other driving spin-reorientation transitions both within and between the planes. The corresponding sequence of magnetic orders unraveled by neutron diffraction and M\"ossbauer spectroscopy features two orthogonal magnetic structures described by opposite local vector chiralities, and an intermediate, partly disordered phase with nearly collinear spins. A similar collinear phase has been predicted theoretically to be stabilized by quantum fluctuations, but Bi$_4$Fe$_5$O$_{13}$F is very far from the relevant parameter regime. While the observed in-plane reorientation cannot be explained by any standard frustration mechanism, our ab initio band-structure calculations reveal strong single-ion anisotropy of the interlayer Fe$^{3+}$ spins that turns out to be instrumental in controlling the local vector chirality and the associated interlayer order.